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A free and open-source calculus textbook

August 13, 2012, 8:00 am

Allow me to make a shameless plug for a very cool project currently underway by my GVSU colleague Matt Boelkins. He is writing a free, open-source calculus textbook that will be available in PDF form online for anyone to use and for any instructor to modify. He has already written the differential calculus portion of the textbook — his Winter semester sabbatical project — and he’s about to begin work on the integral calculus portion. You can download the differential calculus parts here. This is at his blog, where he is promoting the book and soliciting feedback. Matt’s also on Twitter.

Matt and I have talked about this project a lot in the last several months, and I’m deeply impressed by his vision for what this resource could become. He sums it up in this blog post:

While on sabbatical during the winter semester of 2012, I began drafting a free, open-source calculus text. I undertook the project in part because I felt like there wasn’t an activity-driven text available, as well as because I don’t think anyone should make millions by selling a calculus text.

The book that is underway is different from most existing texts in at least the following ways:

  • the text will be free for download by students and instructors in .pdf format;
  • due to the electronic format, graphics are in full color and there are live html links to java applets;
  • the text will (eventually) be open source — interested instructors can gain access to the original source files upon request;
  • the style of the text requires students to be active learners … there are very few worked examples in the text, with there instead being 3–4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas;
  • each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class;
  • the exercises are few in number and challenging in nature.

I’ve looked closely at Matt’s book, and there are two things that really make it stand out for me. One is the deliberate sparsity of examples and exercises. At first glance, this would seem like a flaw. But Matt has apprehended an important concept and codified it in his book: giving more examples does not lead naturally to improved student learning. What’s better than more examples is a few, well-designed examples that get to the heart of a concept and which are done in a way that help students understand simple ideas deeply.

If you’re a factory worker trying to learn a mechanical, rote procedure that you will be replicating on the factory floor hundreds of times a day, every working day for many years, then the more examples you get of that procedure, the better. But calculus is not such a procedure. Or at least it shouldn’t be. Giving more examples makes students feel as if they understand calculus. But a feeling of understanding and true understanding are not the same thing. True understanding takes a much different path, and although a minimalist approach seems counterintuitive, I think it sets students on the right path.

The second thing is that Matt’s book is designed to be consumed by students prior to the beginning of class. It is set up very similarly to the book for our transition-to-proof course — not coincidentally, also written by a GVSU faculty member — with focus questions, preview activities, progress checks, and so on. This is not a static reference book but a resource that should be used early and often. I have never tried to take the inverted classroom approach to calculus because none of the books I have ever seen offer any real hope that students will read and understand them outside of class. You can’t “flip” a classroom without such a resource. Matt’s book may be the first calculus book I’ve seen that has a shot at being understood outside of class — in fact, it’s really supposed to be read and understood outside of class. If students aren’t reading and engaging with the material successfully prior to class, you’re doing it wrong.

Matt’s conviction that textbook materials on calculus ought to be free, and that nobody should get rich selling calculus books, also resonates with me. Three years ago, I wrote this blog post about James Stewart’s $24 million Toronto mansion — even that word fails to capture the opulence of it. I half-jokingly said at the time that if you’re a student and just paid for Stewart’s Calculus, you should consider yourself part-owner of his house and drop in for sushi unannounced some time. Then I suggested that now that Stewart had built his dream home, he should cement his legacy as a Good Guy by making his book freely available online as a PDF.

I was roundly criticized for that, mostly by commenters who turned out to be published authors and publishing company workers, who felt is was unconscionable for somebody to work so hard as to write a calculus book and then just give it away, as if people should just have it for free! I’ve always been puzzled by their shock — except for those times when I heard about people making $150K a year on royalties, textbook companies spending tens of thousands to fly in professors from around the country for focus groups at five-star resorts*, and the sheer waste of sending out unsolicited paper copies of books to professors who didn’t even request them**. Then I realize that to understand the shock, follow the money. (It was also clear that some of these people had never read a blog post before — including the one they were commenting on — but that’s not the point here.)

Matt’s book is cutting through this by laying down a gauntlet: He’s making a quality calculus book and giving it away, not only the book but the source for the book too. He’s not the first person to do this. But I think his project may stand a chance of gaining considerable market share because Matt is a very smart guy, an excellent writer, and above all a gifted teacher. If you teach calculus or are interested in learning it, follow Matt’s blog and Twitter stream and check out his book. It’ll be worth your time.

* This happened. Ask Matt. 

** This also happened. I once got two identical copies of the same massive tome on statistics in the US mail, on the same day, without my solicitation. I don’t even teach stats. 

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